Question

Question Question 4 of 6 (1.7 points) View problem in a pon-UR 6.3 Section Exercise 22 (calc) High-rent district: The mean monthly rent for a one bedroom apartment without a doorman in Manhattan is 52674. Assume the standard deviation is $508. A real estate firm samples 108 apartments. Use the TI-84 calculator: Check Ans Solve It Guided Solu Part 1 What is the probability that the sample mean rent is greater than $2744? Round the answer to four decimal places. Show Exam The probability that the sample mean rent is greater than $2744 is 0.0761 - Tables Formula Part 2 out of 5 What is the probability that the sample mean rent is between S2543 and $2643? Round the answer to four decimal places. The probability that the sample mean rent is between $2543 and $2643 is Save for La Submit Assignme CHECK NIX

Answer 1

Mean, µ = 2674

Standard deviation, σ = 508

Sample size, n = 108

1) Probability that the mean is greater than 2744, P(X̅ > 2744) =

= P( (X̅-μ)/(σ/√n) > (2744-2674)/(508/√108) )

= P(z > 1.432)

= 1 - P(z < 1.432)

Using excel function:

= 1 - NORM.S.DIST(1.432, 1)

= 0.0761

b) Probability that the mean is between 2543 and 2643, P(2543 < X < 2643) =

= P( (2543-2674)/508 < (X-µ)/σ < (2643-2674)/508 )

= P(-0.2579 < z < -0.061)

= P(z < -0.061) - P(z < -0.2579)

Using excel function:

= NORM.S.DIST(-0.061, 1) - NORM.S.DIST(-0.2579, 1)

= 0.0774